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Simplifying 8x2 + 39x + 34 = 0 Reorder the terms: 34 + 39x + 8x2 = 0 Solving 34 + 39x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 4.25 + 4.875x + x2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + 4.875x + -4.25 + x2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + 4.875x + x2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + 4.875x + x2 = 0 + -4.25 4.875x + x2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 4.875x + x2 = -4.25 The x term is 4.875x. Take half its coefficient (2.4375). Square it (5.94140625) and add it to both sides. Add '5.94140625' to each side of the equation. 4.875x + 5.94140625 + x2 = -4.25 + 5.94140625 Reorder the terms: 5.94140625 + 4.875x + x2 = -4.25 + 5.94140625 Combine like terms: -4.25 + 5.94140625 = 1.69140625 5.94140625 + 4.875x + x2 = 1.69140625 Factor a perfect square on the left side: (x + 2.4375)(x + 2.4375) = 1.69140625 Calculate the square root of the right side: 1.300540753 Break this problem into two subproblems by setting (x + 2.4375) equal to 1.300540753 and -1.300540753.Subproblem 1
x + 2.4375 = 1.300540753 Simplifying x + 2.4375 = 1.300540753 Reorder the terms: 2.4375 + x = 1.300540753 Solving 2.4375 + x = 1.300540753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4375' to each side of the equation. 2.4375 + -2.4375 + x = 1.300540753 + -2.4375 Combine like terms: 2.4375 + -2.4375 = 0.0000 0.0000 + x = 1.300540753 + -2.4375 x = 1.300540753 + -2.4375 Combine like terms: 1.300540753 + -2.4375 = -1.136959247 x = -1.136959247 Simplifying x = -1.136959247Subproblem 2
x + 2.4375 = -1.300540753 Simplifying x + 2.4375 = -1.300540753 Reorder the terms: 2.4375 + x = -1.300540753 Solving 2.4375 + x = -1.300540753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4375' to each side of the equation. 2.4375 + -2.4375 + x = -1.300540753 + -2.4375 Combine like terms: 2.4375 + -2.4375 = 0.0000 0.0000 + x = -1.300540753 + -2.4375 x = -1.300540753 + -2.4375 Combine like terms: -1.300540753 + -2.4375 = -3.738040753 x = -3.738040753 Simplifying x = -3.738040753Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.136959247, -3.738040753}
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